harmony. The simultaneous sounding (i.e. combination) of notes, giving what is known as vertical mus., contrasted with horizontal mus. (counterpoint). Composers, in much the greater proportion of their mus., maintain in their minds some melody which ranks as the principal one, and which they intend the listener to recognize as such, whilst other melodies which are combined with it, or chords with which it is acc., rank as subsidiary. The word chord may be defined as any combination of notes simultaneously perf., and even when the main process in the composer's mind is a weaving together of melodic strands he has to keep before him this combinational element, both as regards the notes thus sounded together and the suitability of one combination to follow and precede the adjacent combination.

At different periods composers have given more attention to one or the other of the two aspects of their work: (a) the weaving together of melodic strands and (b) the chords thus brought into existence from point to point.

The former aspect of the result is the contrapuntal element (see counterpoint) and the latter the harmonic element. In less elaborate mus. (as, for instance, a simple song with pf. acc.) the contrapuntal element may be unimportant or even non-existent. Counterpoint necessarily implies also harmony, but harmony does not necessarily imply counterpoint.

Over a long period the resources of harmony may be said to have widened: new combinations introduced by composers of pioneering spirit have been condemned by unaccustomed ears as ugly, have then gradually come to be accepted as commonplace, and have been succeeded in their turn by other experimental combinations. The following definitions concern traditional and basic harmonic procedures:(a) DIATONIC HARMONY: harmony which confines itself to the major or minor key in force at the moment. CHROMATIC HARMONY: harmony which employs notes extraneous to the major or minor key in force at the moment.(b) OPEN HARMONY: harmony in which the notes of the chords are more or less widely spread. CLOSE HARMONY: harmony in which the notes of the chords lie near together.(c) PROGRESSION: the motion of one note to another note or one chord to another chord.(d) TRIAD: a note with its 3rd and 5th (e.g. C-E-G). COMMON CHORD: a triad of which the 5th is perfect. MAJOR COMMON CHORD: a common chord of which the 3rd is major. MINOR COMMON CHORD: a common chord of which the 3rd is minor. AUGMENTED TRIAD: a triad of which the 5th is augmented. DIMINISHED TRIAD: a triad of which the 5th is diminished.(e) ROOT of a chord: that note from which it originates (e.g., in the common chord C-E-G we have C as the root, to which are added the 3rd and 5th). INVERSION of a chord: the removal of the root from the bass to an upper part. FIRST INVERSION: that in which the 3rd becomes the bass (e.g. E-G-C or E-C-G). SECOND INVERSION: that in which the 5th becomes the bass (e.g. G-E-C or G-C-E). THIRD INVERSION: in a 4-note chord that inversion in which the fourth note becomes the bass (e.g., in the chord G-B-D-F the form of it that consists of F-G-B-D or F-B-G-D, etc.). FUNDAMENTAL BASS: an imaginary bass of a passage, consisting not of its actual bass notes but of the roots of its chords, i.e. the bass of its chords when uninverted.(f) CONCORD: a chord satisfactory in itself (or an interval that can be so described; or a note which forms a part of such an interval or chord). CONSONANCE: the same as concord. DISCORD: a chord which is restless, requiring to be followed in a particular way if its presence is to be justified by the ear (or the note or interval responsible for producing this effect). See, for instance, the examples given under dominant (seventh) and diminished (seventh). DISSONANCE: the same as discord. RESOLUTION: the satisfactory following of a discordant chord (or the satisfactory following of the discordant note in such a chord). SUSPENSION: a form of discord arising from the holding over of a note in one chord as a momentary (discordant) part of the combination which follows, it being then resolved by falling a degree to a note which forms a real part of the second chord. DOUBLE SUSPENSION: the same as the last with 2 notes held over.(g) ANTICIPATION: the sounding of a note of a chord before the rest of the chord is sounded. RETARDATION: the same as a suspension but resolved by rising a degree.PREPARATION: the sounding in one chord of a concordant note which is to remain (in the same ‘part’) in the next chord as a discordant note. (This applies both to fundamental discords and suspensions.)UNPREPARED SUSPENSION: a contradiction in terms meaning an effect similar to that of suspension but without ‘preparation’.FUNDAMENTAL DISCORD: a discordant chord of which the discordant note forms a real part of the chord, i.e. not a mere suspension, anticipation, or retardation. Or the said discordant note itself (e.g. dominant seventh, diminished seventh, etc.).PASSING NOTE: a connecting note in one of the melodic parts (not forming a part of the chord which it follows or precedes).(h) FALSE RELATION: the appearance of a note with the same letter-name in different parts (or ‘voices’) of contiguous chords, in one case inflected (sharp or flat) and in the other uninflected.(i) PEDAL (or ‘point d'orgue’): the device of holding on a bass note (usually tonic or dominant) through a passage including some chords of which it does not form a part. INVERTED PEDAL: the same as the above but with the held note in an upper part. DOUBLE PEDAL: a pedal in which two notes are held (generally tonic and dominant).

From Wagner onwards the resources of harmony have been enormously extended, and those used by composers of the present day often submit to no rules whatever, being purely empirical, or justified by rules of the particular composer's own devising. Among contemp. practices are:

Bitonality—in which two contrapuntal strands or ‘parts’ proceed in different keys.

Polytonality—in which the different contrapuntal strands, or ‘parts’, proceed in more than one key.

Atonality—in which no principle of key is observed.

Microtonality—in which scales are used having smaller intervals than the semitone.

In the 20th cent. greater freedom in the treatment of the above procedures has developed, together with a much wider application of dissonance. Chords of 7th, 9th, 11th, and 13th are treated as primary chords, and there has been a return to the use of pentatonic scales, medieval modes, and the whole-tone scale. A prin. revolution c.1910 was the abandonment of the triad as the prin. and fundamental consonance. Composers such as Bartók, Stravinsky, Schoenberg, and Webern widened the mus. spectrum of tone-colour by showing that any combination of notes could be used as a basic unresolved chord. The tritone has been used as the cause of harmonic tensions in place of tonic-dominant relationships. Another 20th-cent. harmonic feature is the ‘layering’ of sound, each layer following different principles of organization. Milhaud produces bitonal passages from two layers in different tonalities.

Since 1950 much mus. has been comp. in which harmony has hardly any place, for example in some of the serial works of Boulez and Stockhausen. Where non-pitched sounds are used, harmony no longer exists and its place is taken by overtones, densities, and other concomitants of ‘clusters’, etc.

In amplification of this entry see added sixth, augmented, consecutive, counterpoint, and chromatic intervals.